asapbleh
  • asapbleh
I don't understand the concept for Infinite Limits.
Calculus1
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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asapbleh
  • asapbleh
For infinite limits, I know that there are as lim x goes to a from the right = +or - infinity
asapbleh
  • asapbleh
but then i dont get the one sided limits and determining if it is a negative or positive infinity
asapbleh
  • asapbleh
This is from my book: If the values of f(x) increase without bound as x approaches positive infinity or as x approaches negative infinity, then: limit as x apporaches positive infinity of f(x)= positive infinity AND limit as x approaches negative infinity of f(x) = positive infinity

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asapbleh
  • asapbleh
and so i really dont get this.
Psymon
  • Psymon
A lot of the time, if you dont know the graph, you have to actually test points. For example, let's say we have \[\lim_{x \rightarrow 2^{+}}\frac{ x ^{2}+3 }{ x-2 }\] Now we may not immediately know what this graph will do as it approaches the asymptote, but thats fine. Knowing that we are approaching 2 from the right, I would pick two points on the right of 2. You can then see what happens to the y-values. DO they shoot up, down, or barely move. So let's try x = 3 first: \[\frac{ (3)^{2}+3 }{ 3-2 }= 12\] Now let's try 5/2 and see if our graph shoots up even more as to where we can say its clearly going to infinity: \[\frac{ (\frac{ 5 }{ 2 })^{2}+3 }{ \frac{ 5 }{ 2 }-2 }= \frac{ \frac{ 37 }{ 4 } }{ \frac{ 1 }{ 2 } }=18.5 \]Because this was a pretty big jump, I would say its safe to say this goes to positive infinity. Kinda see what I did?
asapbleh
  • asapbleh
OH. so its safer to just plug in points and see if it goes up dramatically or goes down dramatically, cause those points u used were (3,12) and (5/2, 18.5) right?
asapbleh
  • asapbleh
wait, isnt 5/2 less than 3, how come the point on the y is higher than 3,12
Psymon
  • Psymon
It is less than 3, butits CLOSER to 2, meaning we're approaching it from the right like we want.
asapbleh
  • asapbleh
now im confused again cause if its like what u said|dw:1378867810266:dw|
asapbleh
  • asapbleh
oyeah i forgot about the approaching 2 part
Psymon
  • Psymon
Basically yes. Here's the actual graph: |dw:1378867965642:dw| So as you can see, if we were approaching it from the left itd be negative infinity. But I wouldnt automatically know that, id have tested 1 then 1.5 to check. But itsd a way to see :3
asapbleh
  • asapbleh
Can you show me an example where x approaches from the left and its positive infinity?
Psymon
  • Psymon
Yeah, sure :3 I just gotta invent one, so give me a second to see if I can think of one that I can guarantee will do that xD
asapbleh
  • asapbleh
Lol. You use the awesome faces. Reminds me of a game. (got off topic) haha =3
Psymon
  • Psymon
Alright, I kinda just reversed the one we just had. Hadto be sure itd do what I want it to do, though. So let's use this: \[\lim_{x \rightarrow 2^{-}}\frac{ 3-x ^{2} }{ x-2 } \]So now that we're coming from the left, I will use two numbers to the left of 2. Ill choose 1 and then 3/2. So starting with x = 1: \[\frac{ 3-(1)^{2} }{ 1-2 }=-2 \]Now Ill check 3/2 \[\frac{ 3-(\frac{ 3 }{ 2 })^{2} }{ \frac{ 3 }{ 2 }-2 }=\frac{ \frac{ 3 }{ 4 } }{ \frac{ -1 }{ 2 } }=\frac{ -3 }{ 2 }\]Okay, we didnt go up very much, but we did get positive. Now I would note now, because it went up a small bit, I would NOT assume positive infinity. Sometimes there is a numerical limit. So Im going to check super close. Now this is done with a calculator just to save time of explaining, but Ill choose 1.95 \[\frac{ 3-(1.95)^{2} }{ 1.95-2 }=\frac{ -.8025 }{ -.05 }=16.05 \] Okay, now we really shot up for sure. So because of that I would definitely say positive infinity. |dw:1378868637002:dw|
asapbleh
  • asapbleh
Oh, I see so basically the closer you get to the asymptote and when you plug it in, it will probably get the line either shooting positive or negative and then you can determine it? i see i see. thanks
Psymon
  • Psymon
Yep, absolutely. But I do have an example of something we have to be careful of. If you have time and want me to show.
asapbleh
  • asapbleh
Of course. I want as much info as i need. I have a test next week. haha

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